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3The 30th International Conference on Advanced Laser Technologies P-O-4
ALT'23
Stochastic approach to describing non-Markovian dynamics of low-
dimensional quantum systems
A. Pavelev1, S. Kharitonov1
1- Samara University, 34, Moskovskoye shosse, Samara, 443086, Russia Main author email address: 44dragon44@rambler.ru
Low-dimensional quantum systems are of great interest from a research perspective as they serve as the physical foundation for quantum computing, quantum metrology, and quantum communication. Since low-dimensional quantum systems interact with the environment, they are essentially open quantum systems [1]. Interaction with the environment is commonly modeled using the simplified Markov approximation [2]. However, experimental evidence suggests that non-Markovian relaxation also occurs in open quantum systems and controlled transitions from Markovian to non-Markovian regimes can be observed [3]. In this report, we present a method for modeling non-Markovian dynamics of low-dimensional quantum systems by incorporating an Ornstein-Uhlenbeck process to modify the stochastic Schrodinger equation [4]. This approach enables numerical modeling of the non-Markovian relaxation dynamics of open quantum systems and their spectral characteristics. We provide modified equations, numerical solution schemes, and simulation results for specific environmental parameters.
Furthermore, we demonstrate how considering the non-Markovian nature of the environment can alter the equilibrium position for the probability of detecting the system in a certain energy state for a three-level system and dipole-dipole interacting qubits. We also illustrate the differences between the resonance fluorescence spectrum of a two-level atom in the Markovian and non-Markovian relaxation regimes. The aim of this report is to discuss the advantages and disadvantages of the stochastic approach for describing relaxation of open quantum systems using numerical modeling of specific systems.
[1] H. Breuer et al. The theory of open quantum systems (Oxford University), (2002).
[2] G. Lindblad, On the generators of quantum dynamical semigroups. Communications in Mathematical Physics, 48., pp. 119-130, (1976).
[3] B. Liu et al., Experimental control of the transition from Markovian to non-Markovian dynamics of open quantum systems, Nature Physics 7(12)., pp. 931-934, (2011).
[4] A Pavelev and V. Semin, Investigation of non-markovian dynamics of two dipole-dipole interacting qubits based on numerical solution of the nonlinear stochastic Schrodinger equation. Computer Optics, 43(2), pp. 168-173, (2019).
